Solve sqrt{200}+sqrt{50}

$$\sqrt{ 200 } + \sqrt{ 50 }$$

Evaluate

$$15\sqrt{2}\approx 21.213203436$$

Solution Steps

Factor 200=10^{2}\times 2. Rewrite the square root of the product \sqrt{10^{2}\times 2} as the product of square roots \sqrt{10^{2}}\sqrt{2}. Take the square root of 10^{2}.

$$10\sqrt{2}+\sqrt{50}$$

Factor 50=5^{2}\times 2. Rewrite the square root of the product \sqrt{5^{2}\times 2} as the product of square roots \sqrt{5^{2}}\sqrt{2}. Take the square root of 5^{2}.

$$10\sqrt{2}+5\sqrt{2}$$

Combine 10\sqrt{2} and 5\sqrt{2} to get 15\sqrt{2}.

$$15\sqrt{2}$$